### Abstract

We establish a singular perturbation result for quasi-linear hyperbolic systems in a bounded domain of R^{3}, depending on a small parameter. We prove and estimate the rate of convergence, as the parameter tends to zero, of uniformly stable solutions of the complete system to a solution of the reduced system. This result is then applied to the study of the convergence of the complete Maxwell equations to the quasi-stationary ones.

Original language | English |
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Pages (from-to) | 111-129 |

Number of pages | 19 |

Journal | Pacific Journal of Mathematics |

Volume | 116 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 1985 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Cite this

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**Singular limits of quasi-linear hyperbolic systems in a bounded domain of R ^{3} with applications to Maxwell’s equations.** / Milani, Albert.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Singular limits of quasi-linear hyperbolic systems in a bounded domain of R3 with applications to Maxwell’s equations

AU - Milani, Albert

PY - 1985/1/1

Y1 - 1985/1/1

N2 - We establish a singular perturbation result for quasi-linear hyperbolic systems in a bounded domain of R3, depending on a small parameter. We prove and estimate the rate of convergence, as the parameter tends to zero, of uniformly stable solutions of the complete system to a solution of the reduced system. This result is then applied to the study of the convergence of the complete Maxwell equations to the quasi-stationary ones.

AB - We establish a singular perturbation result for quasi-linear hyperbolic systems in a bounded domain of R3, depending on a small parameter. We prove and estimate the rate of convergence, as the parameter tends to zero, of uniformly stable solutions of the complete system to a solution of the reduced system. This result is then applied to the study of the convergence of the complete Maxwell equations to the quasi-stationary ones.

UR - http://www.scopus.com/inward/record.url?scp=84972569424&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972569424&partnerID=8YFLogxK

U2 - 10.2140/pjm.1985.116.111

DO - 10.2140/pjm.1985.116.111

M3 - Article

VL - 116

SP - 111

EP - 129

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

SN - 0030-8730

IS - 1

ER -